Write down the boundary-layer equations for steady two-dimensional flow of a viscous incompressible fluid with velocity $U(x)$ outside the boundary layer. Find the boundary layer thickness $\delta(x)$ when $U(x)=U_{0}$, a constant. Show that the boundarylayer equations can be satisfied in this case by a streamfunction $\psi(x, y)=g(x) f(\eta)$ with suitable scaling function $g(x)$ and similarity variable $\eta$. Find the equation satisfied by $f$ and the associated boundary conditions.

Find the drag on a thin two-dimensional flat plate of finite length $L$ placed parallel to a uniform flow. Why does the drag not increase in proportion to the length of the plate? [You may assume that the boundary-layer solution is applicable except in negligibly small regions near the leading and trailing edges. You may also assume that $f^{\prime \prime}(0)=0.33$.]